Simplify the following expression: $ q = -10 + \dfrac{r - 7}{-5r - 2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5r - 2}{-5r - 2}$ $ \dfrac{-10}{1} \times \dfrac{-5r - 2}{-5r - 2} = \dfrac{50r + 20}{-5r - 2} $ Therefore $ q = \dfrac{50r + 20}{-5r - 2} + \dfrac{r - 7}{-5r - 2} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{50r + 20 + r - 7}{-5r - 2} $ $q = \dfrac{51r + 13}{-5r - 2}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-51r - 13}{5r + 2}$